This paper belongs to a series of works to solve inverse problems for nonlinear partial differential equations [1]}, [2]}, [3]}.
In particular, we aim to globally solve an inverse source problem for nonlinear parabolic equations.
By “globally", we mean that our algorithm does not require a priori knowledge of the true solution.
This feature is a significant strength of our method in comparison to the widely-used methods based on least square optimizations, which are locally convergent.
Let \(d \ge 2\)  be the spatial dimension.
Let \(F: \mathbb {R}^d \times \mathbb {R}\times \mathbb {R}^d \rightarrow \mathbb {R}\)  be a function in the class \(C^1(\overline{\Omega })\)  and \(T\)  be a positive number.
Consider the following initial value problem of nonlinear parabolic equation
\(\left\lbrace \begin{array}{ll}u_t = \Delta u + F({\bf x}, u, \nabla u) &({\bf x}, t) \in \mathbb {R}^d \times (0, T),\\u({\bf x}, 0) = p({\bf x}) &{\bf x}\in \mathbb {R}^d.\end{array}\right.\) 
